Question: The function $f$ is linear and satisfies $f(d+1)-f(d) = 3$ for all real numbers $d$. What is $f(3)-f(5)$?
Taking $d = 3,$ we get
\[f(4) - f(3) = 3.\]Taking $d = 4,$ we get
\[f(5) - f(4) = 3.\]Adding these equations, we get $f(5) - f(3) = 6,$ so $f(3) - f(5) = \boxed{-6}.$